5×3-32×2-36x-95x+3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 |
Divide the highest order term in the dividend 5×3 by the highest order term in divisor 5x.
| x2 | |||||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 |
Multiply the new quotient term by the divisor.
| x2 | |||||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| + | 5×3 | + | 3×2 |
The expression needs to be subtracted from the dividend, so change all the signs in 5×3+3×2
| x2 | |||||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| x2 | |||||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 |
Pull the next terms from the original dividend down into the current dividend.
| x2 | |||||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x |
Divide the highest order term in the dividend -35×2 by the highest order term in divisor 5x.
| x2 | – | 7x | |||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x |
Multiply the new quotient term by the divisor.
| x2 | – | 7x | |||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| – | 35×2 | – | 21x |
The expression needs to be subtracted from the dividend, so change all the signs in -35×2-21x
| x2 | – | 7x | |||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| x2 | – | 7x | |||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x | ||||||||
| – | 15x |
Pull the next terms from the original dividend down into the current dividend.
| x2 | – | 7x | |||||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x | ||||||||
| – | 15x | – | 9 |
Divide the highest order term in the dividend -15x by the highest order term in divisor 5x.
| x2 | – | 7x | – | 3 | |||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x | ||||||||
| – | 15x | – | 9 |
Multiply the new quotient term by the divisor.
| x2 | – | 7x | – | 3 | |||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x | ||||||||
| – | 15x | – | 9 | ||||||||
| – | 15x | – | 9 |
The expression needs to be subtracted from the dividend, so change all the signs in -15x-9
| x2 | – | 7x | – | 3 | |||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x | ||||||||
| – | 15x | – | 9 | ||||||||
| + | 15x | + | 9 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| x2 | – | 7x | – | 3 | |||||||
| 5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||
| – | 5×3 | – | 3×2 | ||||||||
| – | 35×2 | – | 36x | ||||||||
| + | 35×2 | + | 21x | ||||||||
| – | 15x | – | 9 | ||||||||
| + | 15x | + | 9 | ||||||||
| 0 |
Since the remander is 0, the final answer is the quotient.
x2-7x-3
Divide (5x^3-32x^2-36x-9)/(5x+3)
